Units
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Topics
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Unit 1: Sets, relations and functions |
- Sets and their representation
- Union, intersection and complement of sets and their algebraic properties
- Power set; Relation, Types of relations, equivalence relations, functions; One-one, into and onto functions, the composition of functions.
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Unit 2: Complex numbers and quadratic equations |
- Complex numbers as ordered pairs of reals,
- Representation of complex numbers in the form a+ib and their representation in a plane,
- Argand diagram,
- algebra of complex numbers,
- modulus and argument (or amplitude) of a complex number,
- square root of a complex number,
- triangle inequality,
- Quadratic equations in real and complex number system and their solutions.
- Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
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Unit 3: Matrices and determinants |
- Matrices,
- algebra of matrices,
- types of matrices,
- determinants and
- matrices of order two and three.
- Properties of determinants,
- evaluation of determinants,
- area of triangles using determinants.
- Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations,
- Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
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Unit 4:
Permutations and combinations |
- Fundamental principle of counting,
- permutation as an arrangement and
- combination as selection,
- Meaning of P (n,r) and C (n,r),
- simple applications.
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Unit 5: Mathematical induction |
- Principle of Mathematical Induction and its simple applications
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Unit 6: Binomial theorem and its simple applications |
- Binomial theorem for a positive integral index,
- general term and middle term,
- properties of Binomial coefficients
- simple applications
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Unit 7: Sequences and series |
- Arithmetic and Geometric progressions,
- insertion of arithmetic,
- geometric means between two given numbers
- relation between A.M. and G.M. sum upto n terms of special series: Sn, Sn2, Sn3
- Arithmetic – Geometric progression
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UNIT 8: Limit, continuity and differentiability |
- Real – valued functions,
- algebra of functions,
- polynomials,
- rational,
- trigonometric,
- logarithmic and exponential functions,
- inverse functions
- Graphs of simple functions
- Limits, continuity and differentiability
- Differentiation of the sum, difference, product and quotient of two functions
- Differentiation of trigonometric,
- inverse trigonometric,
- logarithmic,
- exponential,
- composite and implicit functions
- derivatives of order upto two
- Rolle’s and Lagrange’s Mean Value Theorems
- Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions,
- Maxima and minima of functions of one variable,
- tangents and normals
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Unit 9: Integral calculus |
- Integral as an anti – derivative.
- Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.
- Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.
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- Evaluation of simple integrals of the type Integral as limit of a sum.

- Fundamental Theorem of Calculus.
- Properties of definite integrals.
- Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
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Unit 10: Differential equations |
- Ordinary differential equations, their order and degree.
- Formation of differential equations.
- Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x)
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Unit 11: Co-ordinate geometry |
- Cartesian system of rectangular co-ordinates 10 in a plane,
- distance formula,
- section formula,
- locus and its equation,
- translation of axes,
- slope of a line,
- parallel and perpendicular lines,
- intercepts of a line on the coordinate axes.
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Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines. |
Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency. |
Unit 12: Three dimensional geometry |
- Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines.
- Skew lines, the shortest distance between them and its equation.
- Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.
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Unit 13: Vector algebra |
- Vectors and scalars,
- addition of vectors,
- components of a vector in two dimensions and three dimensional space,
- scalar and vector products, scalar and vector triple product.
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Unit 14: Statistics and probability |
Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution. |
Unit 15: Trigonometry |
- Trigonometrical identities and equations
- Trigonometrical functions
- Inverse trigonometrical functions and their properties
- Heights and Distances
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Unit 16: Mathematical reasoning |
- Statements, logical operations and, or, implies, implied by, if and only if
- Understanding of tautology, contradiction, converse and contrapositive
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